TMJC (Supplementary) SLS Learning Experience - Exploration of Basic Transformations (Filled in Copy)

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 1 of 12 H2 Mathematics (9758) Chapter 2 Transformations of Curves Learning Experience 1 Exploration of Basic Transformations Filled-in Copy Success Criteria: Surface Learning Deep Learning Transfer Learning  Determine the translation units in the positive / negative y-direction by observing the graph using the applet.  Determine the translation units in the positive / negative x-direction by observing the graph using the applet.  Identify whether the transformation involves either the x-value or the y-value.  Determine the stretch factor parallel to x-axis / y-axis by observing the graph using the applet.  Visualise a graph that undergoes a reflection in the x-axis / y-axis using applet.  Identify the replacement of variable involved in translation of a graph (i.e. ( )fy x a=+ & ( )fy x a=+ )  Identify the replacement of variable involved in stretching of a graph (i.e. ( )fyax= & f xy a =  )  Write down the equation of the resultant curve after going through a reflection in the x-axis / y-axis.  Identify the replacement of variable involved in reflecting a graph either in the x-axis or y-axis. Instructions to students: 1. For each applet in Section 1 and 2, move the slider to vary the value of A before writing down your observations. 2. Circle the correct answer where there is an * sign. Slider to vary the value of A

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 2 of 12

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 3 of 12 BASIC TRANSFORMATIONS §1 Translation §1.1 Translation in the direction of y-axis Let ( ) 2 11yx= − + . Using Geogebra, observe the change in the behavior of the graph of ( ) 2 11y x A= − + + when the value of A changes. Activity 1 Observation 1: Describe the change in the graph of ( ) 2 11yx= − + when the value of A increases from 0 to 3. Translation of 3 units in the positive y-direction. Observation 2: Sketch the graph after this transformation. Observation 3: Let (1, 1) be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2. Observation 4: Which value is changed? Observation 5: What is the replacement of variable involved in transforming the graph of ( ) 2 11yx= − + to ( ) 2 1 1 3yx = − + + ? Replace y by (1,4) y-value y − 3

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 4 of 12 Activity 2 Observation 1: Describe the change in the graph of ( ) 2 11y x A= − + + when the value of A decreases from 0 to −2. Translation of 2 units in the negative y-direction. Observation 2: Sketch the graph after this transformation. Observation 3: Let (1,1) be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2. Observation 4: Which value is changed? Observation 5: What is the replacement of variable involved in transforming the graph of ( ) 2 11yx= − + to ( ) 2 1 1 2yx = − + − ? Replace y by (1,−1) y-value y – (−2) = y + 2

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 5 of 12 §1.2 Translation in the direction of x-axis Let ( ) 2 11yx= − + . Using Geogebra, observe the change in the behavior of the graph of ( ) 2 11y x A= + − + when the value of A changes. Activity 1 Observation 1: Describe the change in the graph of ( ) 2 11y x A= + − + when the value of A increases from 0 to 2. Translation of 2 units in the negative x-direction. Observation 2: Sketch the graph after this transformation. Observation 3: Let (1, 1) be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2. Observation 4: Which value is changed? Observation 5: What is the replacement of variable involved in transforming the graph of ( ) 2 11yx= − + to ( ) 2 2 1 1yx= + − + (i.e. ( ) 2 11yx= + + ) ? Replace x by (−1,1) x-value x + 2

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 6 of 12 Activity 2 Observation 1: Describe the change in the graph of ( ) 2 11y x A= + − + when the value of A decreases from 0 to −3. Translation of 3 units in the positive x-direction. Observation 2: Sketch the graph after this transformation. Observation 3: Let (1, 1) be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2. Observation 4: Which value is changed? Observation 5: What is the replacement of variable involved in transforming the graph of ( ) 2 11yx= − + to ( ) 2 3 1 1yx= − − + (i.e. ( ) 2 41yx= − + ) ? Replace x by (4,1) x-value x − 3

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 7 of 12 §2 Stretch §2.1 Stretch parallel to the y-axis Let ( ) 2 11yx= − + . Using Geogebra, observe the change in the behavior of the graph of ( ) 2 11y A x = − + when the value of A changes. Activity 1 Observation 1: Describe the change in the graph of ( ) 2 11y A x = − + when the value of A increases from 1 to 3. Stretch of factor 3 parallel to the y-axis. Observation 2: Sketch the graph after this transformation. Observation 3: Let ( )1,1 be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2. Observation 4: Which value is changed? Observation 5: What is the replacement of variable involved in transforming the graph of ( ) 2 11yx= − + to ( ) 2 3 1 1yx = − + ? Replace y by ( )1, 3 y-value 3 y

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 8 of 12 Activity 2 Observation 1: Describe the change in the graph of ( ) 2 11y A x = − + when the value of A decreases from 1 to 1 2 . Stretch of factor 1 2 parallel to the y-axis. Observation 2: Sketch the graph after this transformation. Observation 3: Let ( )1,1 be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2. Observation 4: Which value is changed? Observation 5: What is the replacement of variable involved in transforming the graph of ( ) 2 11yx= − + to ( ) 21 112yx = − + ? Replace y by 11, 2   y-value 2 1 2 yy= 

Chapter 2 Transformation of Curves TMJC 2024 Filled-in Copy Page 9 of 12 §2.2 Stretch parallel to the x-axis Let ( ) 2 11yx= − + . Using Geogebra, observe the change in the behavior of the graph of 2 11xy A = − + when the value of A changes. Activity 1 Observation 1: Describe the change in the graph of 2 11xy A = − + when the value of A decreases from 1 to 1 4 . Stretch of factor 1 4 parallel to the x-axis. Observation 2: Sketch the graph after this transformation. Observation 3: Let ( )1,1 be the minimum turning point on the curve ( ) 2 11yx= − + . Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed gr